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A SIMPLE CLOSED-FORM FORMULA FOR PRICING DISCRETELY-SAMPLED VARIANCE SWAPS UNDER THE HESTON MODEL

Part of: Mathematical finance

Published online by Cambridge University Press:  09 October 2014

SANAE RUJIVAN  and
SONG-PING ZHU
SANAE RUJIVAN*
Affiliation:
Division of Mathematics, School of Science, Walailak University, Nakhon Si Thammarat 80161, Thailand email [email protected]
SONG-PING ZHU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email [email protected]
*
✉[email protected]
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Abstract

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We develop a simplified analytical approach for pricing discretely-sampled variance swaps with the realized variance, defined in terms of the squared log return of the underlying price. The closed-form formula obtained for Heston’s two-factor stochastic volatility model is in a much simpler form than those proposed in literature. Most interestingly, we discuss the validity of our solution as well as some other previous solutions in different forms in the parameter space. We demonstrate that market practitioners need to be cautious, making sure that their model parameters extracted from market data are in the right parameter subspace, when any of these analytical pricing formulae is adopted to calculate the fair delivery price of a discretely-sampled variance swap.

Keywords

variance swapsHeston modelclosed-form exact solutionstochastic volatility

MSC classification

Secondary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 1 , July 2014 , pp. 1 - 27
Copyright
Copyright © 2014 Australian Mathematical Society 

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